The first Tube strike over pay will coincide with local elections on 10 June, the Rail Maritime and Transport Union (RMT) has announced.
A strike could cause chaos for millions of travellers
It is expected to be the first in a series of walkouts which will cripple London Underground (LU).
The announcement was made after RMT members backed industrial action by 2,614 to 643 on Wednesday.
The union is seeking a "substantial" pay rise, having rejected a 3% offer earlier, and a cut in hours.
A strike by thousands of signallers, maintenance and station staff and some drivers belonging to the RMT would cause severe disruption on the Tube, which is used by three million people every day.
It could also cause havoc for those attempting to vote in the mayoral, London Assembly and European Parliament elections.
The union's general secretary Bob Crow said the members' vote gave an "overwhelming mandate" for strikes.
He said: "This pay round should have been settled by April but here we are, two months later, with an unresolved dispute.
"If the employers are sincere in wanting to avoid strike action, the answer remains in their hands - they must stop messing around and negotiate seriously."
As well as the pay rise, the union is seeking a cut in working hours to 32 a week.
London Underground said it had written to the unions with a revised offer and was ready to continue negotiations.
A spokesman said: "We remain committed to reaching an agreement with the unions and we are working with them to meet as soon as practicable."
Metronet, one of the private companies that maintains part of the network, issued a 3% pay rise to its 5,000 Tube workers last week.
This was over its original 2.4% offer and backdated to 1 April.
It also mooted the possibility of a further increase linked to flexibility, productivity and efficiency gains.